MDG: Dayag and Dayan come from the exact same root. In fact, most jobs can be described in the same way. Take a noun or a verb, put a Patach under the first letter and a Kamatz (with a Dagesh) in the second. This is common through Mishnaic Hebrew. All Ben Yegudah did was standardize that.
And R’ Schachter quotes a Maharil that we are not Mapkid on Mil’eil and Mil’rah even where it changes the meaning. I think, however, that this is a Limud Z’chus at best. I have long thought that someone who habitually messes up Mil’eils and Mil’ras is only Yotzei as a Loez and not as a Korei B’lashon Hakodesh.